When to Review Welchs Test Vs Kruskal Wallis Test

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A Kruskal-Wallis test is used to determine whether or not there is a statistically significant deviation between the medians of three or more contained groups.

This test is the nonparametric equivalent of the i-manner ANOVA and is typically used when the normality assumption is violated.

The Kruskal-Wallis test does non presume normality in the information and is much less sensitive to outliers than the one-fashion ANOVA.

Hither are a couple examples of when you lot might behave a Kruskal-Wallis test:

Example 1: Comparison Study Techinques

You randomly dissever a class of 90 students into three groups of thirty. Each grouping uses a different studying technique for 1 calendar month to set up for an exam.

At the finish of the month, all of the students take the same exam. You lot want to know whether or not the studying technique has an bear upon on exam scores.

From previous studies you know that the distributions of examination scores for these three studying techniques are not normally distributed so you carry a Kruskal-Wallis examination to determine if there is a statistically meaning departure between the median scores of the three groups.

Example ii: Comparing Sunlight Exposure

You want to know whether or not sunlight impacts the growth of a certain found, then you institute groups of seeds in four different locations that experience either high sunlight, medium sunlight, low sunlight or no sunlight.

After i month you mensurate the superlative of each grouping of plants. It is known that the distribution of heights for this certain plant is not normally distributed and is decumbent to outliers.

To determine if sunlight impacts growth, you conduct a Kruskal-Wallis test to determine if there is a statistically meaning difference between the median height of the four groups.

Kruskal-Wallis Exam Assumptions

Before we tin conduct a Kruskal-Wallis test, we need to make certain the following assumptions are met:

1. Ordinal or Continuous Response Variable– the response variable should be an ordinal or continuous variable. An example of an ordinal variable is a survey response question measured on a Likert Scale (e.yard. a 5-signal scale from "strongly disagree" to "strongly concord") and an instance of a continuous variable is weight (east.g. measured in pounds).

ii. Independence – the observations in each group need to exist independent of each other. Commonly a randomized design will take care of this.

3. Distributions have similar shapes – the distributions in each group need to take a like shape.

If these assumptions are met, and then we can proceed with conducting a Kruskal-Wallis test.

Example of a Kruskal-Wallis Test

A researcher wants to know whether or not three drugs have different effects on knee pain, so he recruits 30 individuals who all experience similar knee pain and randomly splits them up into three groups to receive either Drug one, Drug ii, or Drug three.

After one month of taking the drug, the researcher asks each individual to rate their knee pain on a calibration of 1 to 100, with 100 indicating the about severe hurting.

The ratings for all 30 individuals are shown below:

Drug ane	Drug two	Drug three
78	71	57
65	66	88
63	56	58
44	forty	78
50	55	65
78	31	61
70	45	62
61	66	44
fifty	47	48
44	42	77

The researcher wants to know whether or not the three drugs have unlike furnishings on knee pain, so he conducts a Kruskal-Wallis Exam using a .05 significance level to make up one's mind if there is a statistically significant difference between the median articulatio genus pain ratings across these three groups.

We can utilize the following steps to perform the Kruskal-Wallis Test:

Footstep 1. State the hypotheses.

The cypher hypothesis (H₀): The median genu-pain ratings across the three groups are equal.

The alternative hypothesis: (Ha): At least one of the median knee-hurting ratings is different from the others.

Step 2. Perform the Kruskal-Wallis Test.

To conduct a Kruskal-Wallis Examination, nosotros tin can simply enter the values shown above into the Kruskal-Wallis Test Computer:

So click the "Calculate" push button:

Step 3. Interpret the results.

Since the p-value of the test (0.21342) is non less than 0.05, we neglect to reject the null hypothesis.

We exercise non have sufficient evidence to say that there is a statistically significant departure between the median knee joint pain ratings beyond these three groups.

Boosted Resources

The following tutorials explain how to perform a Kruskal-Wallis Test using different statistical software:

How to Perform a Kruskal-Wallis Test in Excel
How to Perform a Kruskal-Wallis Test in Python
How to Perform a Kruskal-Wallis Test in SPSS
How to Perform a Kruskal-Wallis Exam in Stata
How to Perform a Kruskal-Wallis Test in SAS
Online Kruskal-Wallis Test Figurer

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Source: https://www.statology.org/kruskal-wallis-test/

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